SME
Propulsion · Problem type
Turbojet thrust and efficiency
Use this for “A turbojet takes in 50 kg/s of air at 250 m/s and jets it out at 600 m/s, burning 0.9 kg/s of fuel. Find F, TSFC and ηₚ.”
Diagram
F = ṁ(Vₑ − V₀) = 50 × (600 − 250)
F = 17,500 N
The
arrows
share
one
scale.
ηₚ
=
2
1 + 600 ÷ 250
=
58.82%.
This is an example. Type your own values to start a new problem.
F (kN)
=
ṁ (kg/s)
×
(
Vₑ (m/s)
−
V₀ (m/s)
)
ṁf
Fuel flow
example · kg/s
TSFC
Thrust-specific fuel consumption
calculated
ηₚ
Propulsive efficiency
calculated · %
Formulas
F
=
ṁ
×
(Vₑ
−
V₀
)
17,500 = 50 × (600 − 250)
TSFC
=
3,600
×
ṁf
F
0.1851
=
3,600
×
0.9
17,500
ηₚ
=
2
1 + Vₑ ÷
V₀
×
100
58.82
=
2
1 + 600 ÷ 250
×
100
Formulas are worked in N. The step-by-step shows the conversions.
Assumptions
•
The exit pressure matches the ambient pressure, so there is no pressure thrust.
•
The fuel’s mass is small beside the air’s and is left out of the momentum.
•
TSFC is in kg of fuel per newton of thrust per hour: 3600 × ṁf ÷ F.
Step-by-step
WE KNOW
ṁ = 50 kg/s, V₀ = 250 m/s, Vₑ = 600 m/s, ṁf = 0.9 kg/s
FIND
thrust (F), thrust-specific fuel consumption (TSFC), propulsive efficiency (ηₚ)
Step 1 · Find thrust (F)
Use F = ṁ × (Vₑ − V₀)
Thrust is the momentum the engine adds to each second’s air.
F
=
50
×
(600
−
250)
F
=
50
×
350
F
=
17,500
N
Step 2 · Find thrust-specific fuel consumption (TSFC)
Use TSFC = 3,600 × ṁf ÷ F
Fuel burned each second per newton of thrust, times 3600 seconds in an hour.
TSFC
=
3,600
×
0.9
17,500
TSFC
=
3,240
17,500
TSFC = 0.1851 kg/(N·h)
Step 3 · Find propulsive efficiency (ηₚ)
Use ηₚ = 2 ÷ (1 + Vₑ ÷ V₀) × 100
Thrust power over the jet’s gain in kinetic energy; times 100 for a percent.
ηₚ
=
2
1 + 600 ÷ 250
×
100
ηₚ
=
2
1 + 2.4
×
100
ηₚ
=
2
3.4
×
100
ηₚ = 0.5882 × 100
ηₚ = 58.82%
Step 4 · Convert the answers
Change each answer back to the unit you chose.
F = 17,500 N = 17.5 kN (1 kN = 1000 N)
Check
Put the numbers back in. Both sides should match.
17,500 = 50 × (600 − 250) ✓
0.1851
=
3,600
×
0.9
17,500
✓
58.82
=
2
1 + 600 ÷ 250
×
100
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Gas turbine cycles
Main lesson
Compressor exit temperature
Use this for “A compressor with ηc = 0.85 takes in air at 300 K and has a pressure ratio of 10. What is its exit temperature?”
Turbofan thrust
Use this for “A turbofan’s core takes 20 kg/s with a bypass ratio of 5 at 230 m/s. The core jet leaves at 500 m/s, the fan jet at 320 m/s. Find its thrust.”